vmd的代码matlab

VMD（Variational Mode Decomposition）是一种信号处理方法，它可以将信号分解成多个本征模态函数（Intrinsic Mode Functions, IMF）。以下是用MATLAB实现VMD的示例代码：

function [u, omega, alpha] = VMD(signal, alpha, tau, K, DC, init, tol)
% signal: input signal
% alpha: balancing parameter
% tau: noise-tolerance (noisy data) or spread of modes (mode mixing)
% K: number of modes to extract
% DC: include (DC = 1) or exclude (DC = 0) the zero-frequency mode
% init: 0 = all omegas start at 0
%       1 = all omegas start uniformly distributed
% tol: tolerance of convergence criterion; typically around 1e-6

u = signal(:)'; % working with row vectors
N = length(u);
t = (1:N)/N;

% FFT parameters
fs = 1/(t(2)-t(1));
f = fs*(0:(N/2)-1)/N;
f = [f, -f(end:-1:1)];

% Construct and center f-range grid for FFT
omega = 2*pi*f;
omega(N/2+1) = 0;
if DC
    K = K+1; % increase mode count if including DC mode
end

% Initialize loop variables
u_hat = fft(u);
u_hat_plus = u_hat;
u_hat_minus = 0*u_hat;
Omega_plus = omega;
Omega_minus = omega;
u_plus = 0*u;
u_minus = 0*u;
k = 1;
energy = Inf;
maxiter = 1000;
it = 0;

% Main loop
while (it < maxiter) && (energy > tol)
    it = it+1;
    % Update first mode u_1 via LP
    if init == 0
        omega_1 = 0;
    else
        omega_1 = rand()*pi;
    end
    u_1 = u;
    for j=1:K-1
        u_hat_plus = ifft(u_hat_minus + omega_1*u_hat);
        u_hat_minus = ifft(u_hat_plus - omega_1*u_hat);
        Omega_plus = Omega_minus + tau*omega_1;
        Omega_minus = Omega_plus - tau*omega_1;
        % Soft thresholding
        u_plus = real(u_hat_plus.*exp(alpha*(abs(Omega_plus)/tau-alpha)));
        u_minus = real(u_hat_minus.*exp(alpha*(abs(Omega_minus)/tau-alpha)));
        % Extract residual
        u_1 = u_1 - u_plus - u_minus;
        % Update omegas via Newton iteration
        omega_1 = omega_1 - (u_hat.*u_hat_minus - conj(u_hat).*u_hat_plus)*...
            (1/(2*tau*(abs(u_hat_plus).^2 + abs(u_hat_minus).^2)));
    end
    % Extract last mode
    u_k = u_1;
    % Calculate energy
    energy = norm(u_k);
    % Save current mode
    u(k,:) = u_k;
    omega(k) = omega_1;
    % Update u_hat and remove current mode
    u_hat = u_hat - fft(u_k);
    k = k+1;
end

% Remove unused entries in arrays
u = u(1:k-1,:);
omega = omega(1:k-1);
alpha = alpha*ones(1,k-1);
end

这里是一个简单的例子，使用上述代码分解一个包含两个正弦波的信号：

% Generate signal
t = linspace(0,1,1024);
s1 = sin(2*pi*60*t);
s2 = sin(2*pi*120*t);
signal = s1 + s2;

% VMD parameters
alpha = 2000; % moderate bandwidth constraint
tau = 0; % noise-tolerance (no strict fidelity enforcement)
K = 2; % 2 modes
DC = 0; % no DC part imposed
init = 1; % initialize omegas uniformly
tol = 1e-6;

% Perform VMD
[u, omega, alpha] = VMD(signal, alpha, tau, K, DC, init, tol);

% Plot results
subplot(K+1,1,1); plot(t,signal); title('Signal');
for k=1:K
    subplot(K+1,1,k+1);
    plot(t,u(k,:)); title(['Mode ' num2str(k)]);
end

这将生成一个包含原始信号和两个本征模态函数的图形。